Layer‑specific spin Hall currents in MnBi₂Te₄ reveal magnetic‑direction‑dependent control of antiferromagnetic order
arXiv: 2610.40215v1
In the antiferromagnetic topological insulator MnBi₂Te₄, first‑principles calculations show that the spin Hall conductivity is split into a magnetization‑independent part and two magnetization‑dependent “spin anomalous Hall” terms that change even if the Néel vector is inverted. This means the torque generated on each septuple layer depends on the local magnetic order, allowing reversible, field‑free switching of the staggered magnetization in few‑layer films when an in‑plane charge current is applied.
Fig 1. Schematic showing how the spin Hall response in MnBi₂Te₄ separates into a magnetization‑independent part (σSHE0) and two magnetization‑dependent “spin anomalous Hall” components (σSAHE1 and σSAHE2) that vary with Néel‑vector orientation.Pan, Sheng, Wang, Weiwei, Yu, Jie-Xiang · arXiv:2610.40215v1 · Fig 1: ·
The calculations employed density‑functional theory with the PBE functional and a Hubbard U correction to obtain the band structure, then constructed a Wannier‑based tight‑binding Hamiltonian. Using the Kubo formula implemented in Wannier90, the layer‑resolved spin Hall conductivity (LSHC) was extracted for each septuple layer. The analysis highlighted that the LSHC contains a constant σSHE0 term and two even functions σSAHE1 and σSAHE2 that depend on the Néel vector components, providing a microscopic description of how spin‑charge conversion varies across the film.
When comparing two‑septuple‑layer (2SL) and four‑septuple‑layer (4SL) films, a striking difference emerges. In 2SLs, the σx component of the spin Hall conductivity is essentially zero for all orientations of the Néel vector, implying little layer‑resolved torque along x. In contrast, 4SLs exhibit a finite σx that varies with the Néel vector orientation in the xz plane, indicating a stronger magnetization‑dependent channel that can redistribute torques and reshape the switching trajectory. This layer‑specific behaviour is quantified in the fitted coefficient tables for each film configuration.
Table listing tilt angles and σSHE0, σSAHE1, σSAHE2 for 2‑SLs total and 4‑SLs surface/inner layers, showing non‑zero σx values only for the 4‑SL inner layer.
System / Layer
Tilt angle θ
𝝈SHE0
𝝈SAHE1
𝝈SAHE2
2 SLs (Total)
0∘
(0,0.65,−0.12)
(0,0.36,0.19)
(0,0,0)
4 SLs surface
≈22∘
(0,0.63,−0.23)
(0,0.53,0.30)
(0.18,0.11,−0.18)
4 SLs inner
≈9∘
(0,0.12,−0.42)
(0,0.77,0.20)
(0.29,0.23,−0.11)
Table 1. Comparison of fitted coefficient vectors for 2‑SL and 4‑SL MnBi₂Te₄ films, highlighting that 2‑SLs have negligible σx for all Néel‑vector orientations, whereas 4‑SLs exhibit a finite, Néel‑vector‑dependent σx component in the xz plane.Pan, Sheng, Wang, Weiwei, Yu, Jie-Xiang · arXiv:2610.40215v1 · Table 1: · CC BY 4.0
Because the bulk conductivity of MnBi₂Te₄ vanishes inside the topological band gap, the charge current needed to drive the simulated spin‑torque switching is one to two orders of magnitude lower than the spin Hall current used in the calculations. Thus, in practice, very small charge currents could suffice to activate spin‑orbit torque–mediated switching, pointing to low‑power operation in future antiferromagnetic spintronic devices.
These findings open a route to tailor current‑driven switching through layer and interface engineering, using the intrinsic magnetization dependence of the spin Hall effect in layered antiferromagnetic topological insulators.
